Being an inter-disciplinary subject, Signal Processing has application in almost all scientific fields. Applied Signal Processing tries to link between the analog and digital signal processing ...domains. Since the digital signal processing techniques have evolved from its analog counterpart, this book begins by explaining the fundamental concepts in analog signal processing and then progresses towards the digital signal processing. This will help the reader to gain a general overview of the whole subject and establish links between the various fundamental concepts. While the focus of this book is on the fundamentals of signal processing, the understanding of these topics greatly enhances the confident use as well as further development of the design and analysis of digital systems for various engineering and medical applications. Applied Signal Processing also prepares readers to further their knowledge in advanced topics within the field of signal processing.
Conventional Fourier-transform infrared (FTIR) microspectroscopic systems are limited by an inevitable trade-off between spatial resolution, acquisition time, signal-to-noise ratio (SNR) and sample ...coverage. We present an FTIR imaging approach that substantially extends current capabilities by combining multiple synchrotron beams with wide-field detection. This advance allows truly diffraction-limited high-resolution imaging over the entire mid-infrared spectrum with high chemical sensitivity and fast acquisition speed while maintaining high-quality SNR.
The discrete fractional Fourier transform (DFRFT) plays an important role in processing time-varying signals. Nevertheless, directly computing the DFRFT involves high complexity, particularly when ...addressing multi-angle DFRFT scenarios. This article presents a method to compute multi-angle DFRFTs through the execution of a single complex DFRFT, exploiting several properties of the DFRFT. We first calculate the DFRFTs with rotation angles 0 and α. Subsequently, when dealing with the DFRFTs of two real signals with rotation angles α and β, which is so-called the multi-angle DFRFTs, our method only need one complex DFRFT and some additional manipulations with complexity O(M), which reduce the computational complexity efficiently. Furthermore, the proposed method is also applicable to the processing of two dimensional (2D) signals. Additionally, as a generalized form of the DFRFT, the fast computation of the multi-angle discrete affine Fourier transform (DAFT) is also considered. Finally, the simulation results confirm that the proposed methods can effectively reduce the computational complexity without compromising precision.
•A method of computing the multi-angle discrete fractional Fourier transform (DFRFT) of two real N -point signals by utilizing the complex N -point DFRFT only once is proposed, which is further generalized to the two-dimensional DFRFT.•Further this method is applied to the computation of the discrete affine Fourier transform.•A key index to a digital transform, the computational complexity of the proposed algorithms are analyzed. And accuracy analysis of the proposed algorithms are introduced.
In this paper, the design of frequency-locked loop (FLL) is proposed based on computationally efficient discrete Fourier transform (DFT) structures. In recent years, the DFT structures are evolved as ...sliding DFT (SDFT), modulated SDFT, hopping DFT (HDFT), modulated HDFT, and sliding-windowed infinite Fourier transform. Considering their tuned filter characteristics, an attempt has been made to obtain a solution for the instantaneous frequency estimation problem of the input signal under varying center frequency condition. In each DFT structure, the <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula>th bin in-phase and quadrature components are separated for instantaneous signal extraction. The feedback loop is designed around these DFT structures, and it was observed that the frequency responses exhibit flat magnitude and phase interestingly when compared with the open-loop structures. Hence, an adaptive sampling frequency adjustment scheme is proposed for these structures as FLL to estimate the instantaneous frequency of the input signal for the wide variation in center frequency. These FLLs with different DFT structures are tested for dynamic performance and wide operating range. The proposed FLLs are implemented in field-programmable gate array (FPGA), and the experimental investigations have been carried out for frequency estimation. Further experimental investigations on these FLLs as a system on chip were carried out with area and power analysis.
In this work, we propose a new substitution scheme for color images watermarking based on the Fourier transform. This scheme will be declined into two variants in which the image will be divided into ...three components R, G and B, and then to each component a transform is applied. The parity of the resulting coefficients will then be combined to hide the watermark in the medium frequency band. In our experiments several variants of the Fourier transform are used (Discrete Fourier Transform, a Fractional Fourier Transform as well as a Quaternion Discrete Fourier Transform). For each transform, both variants of our watermarking scheme are applied. The obtained results show that our approach offers good imperceptibility and generates watermarking images robust against various attacks with a high-quality watermark.
•In the spatial domain a combination between the data value samples provides reasonable SNR results (more than 66dB).•These approaches are simple and inexpensive in computation time can be used for ...real-time watermarking required in low-power environments.•The use of transforms makes the message more robust to compression, since it uses the same space used for coding.•The results obtained remain satisfactory compared to some recent work with a SNR greater than 33dB on average.•The decomposition into sub-bands provides acceptable and satisfactory levels of SNR compared to some recent work with a SNR greater than 40dB.
In this paper; we propose two new substitution schemes for digital audio watermarking based on the Fourier transform. The integration of the watermark will be performed by combining the parity of the successive coefficients values; each variant will represent a different combination. In our experiments several variants of the Fourier transform are used (Discrete Fourier Transform, a Fractional Fourier Transform as well as a Quaternion Discrete Fourier Transform). For each transform, both variants of our watermarking scheme are applied and the results obtained show that our approach offers good imperceptibility and generates watermarked audio sample robust against various attacks with a high-quality watermark. However, using small audio file for our experiments considerably reduces the capacity of our approach in the frequency domain.
As a generalization of the classical Fourier transform (FT), the fractional Fourier transform (FRFT) has proven to be a powerful tool for signal processing and analysis. However, it is not suitable ...for processing signals whose fractional frequencies vary with time due to a lack of time localization information. A simple method to overcome this limitation is the short-time FRFT (STFRFT). There exist several different definitions of the STFRFT in the literature. Unfortunately, these existing definitions do not well generalize the classical result of the conventional short-time FT (STFT), which can be interpreted as a bank of FT-domain filters. The objective of this paper is to propose a novel STFRFT that preserves the properties of the conventional STFT and can be implemented easily in terms of FRFT-domain filter banks. We first present the novel STFRFT and then derive its inverse transform and basic properties. The time-fractional-frequency analysis of this transform is also presented. Moreover, the implementation of the proposed STFRFT is discussed. Finally, we provide several applications for the proposed STFRFT.
Fourier phase retrieval, which aims to reconstruct a signal from its Fourier magnitude, is of fundamental importance in fields of engineering and science. In this paper, we provide a theoretical ...understanding of algorithms for the one-dimensional Fourier phase retrieval problem. Specifically, we demonstrate that if an algorithm exists which can reconstruct an arbitrary signal x∈CN in Poly(N)log(1/ϵ) time to reach ϵ-precision from its magnitude of discrete Fourier transform and its initial value x(0), then P=NP. This partially elucidates the phenomenon that, despite the fact that almost all signals are uniquely determined by their Fourier magnitude and the absolute value of their initial value |x(0)|, no algorithm with theoretical guarantees has been proposed in the last few decades. Our proofs employ the result in computational complexity theory that the Product Partition problem is NP-complete in the strong sense.
The literature on the subject of synchrophasor estimation (SE) algorithms has discussed the use of interpolated discrete Fourier transform (IpDFT) as an approach capable to find an optimal tradeoff ...between SE accuracy, response time, and computational complexity. Within this category of algorithms, this paper proposes three contributions: the formulation of an enhanced-IpDFT (e-IpDFT) algorithm that iteratively compensates the effects of the spectral interference produced by the negative image of the main spectrum tone; the assessment of the influence of the e-IpDFT parameters on the SE accuracy; and the discussion of the deployment of IpDFT-based SE algorithms into field programmable gate arrays, with particular reference to the compensation of the error introduced by the free-running clock of A/D converters with respect to the global positioning system (GPS) time reference. The paper finally presents the experimental validation of the proposed approach where the e-IpDFT performances are compared with those of a classical IpDFT approach and to the accuracy requirements of both P and M-class phasor measurement units defined in the IEEE Std. C37.118-2011.
We present a single synchrophasor estimation (SE) algorithm that is simultaneously compliant with both P and M phasor measurement unit (PMU) performance classes. The method, called ...iterative-interpolated discrete Fourier transform (i-IpDFT), iteratively estimates and compensates the effects of the spectral interference produced by both a generic interfering tone, harmonic or interharmonic, and the negative image of the fundamental tone. We define the three-point i-IpDFT technique for cosine and Hanning window functions and we propose a procedure to select the i-IpDFT parameters. We assess the performance of the i-IpDFT with respect to all the operating conditions defined in the IEEE Std. C37.118 for P- and M-class PMUs. We demonstrate that the proposed SE method is simultaneously compliant with all the accuracy requirements of both PMU performance classes.
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